Electron density fitting sequence

From a map at low resolution (5 A or higher) one can obtain the shape of the molecule and sometimes identify a-helical regions as rods of electron density. At medium resolution (around 3 A) it is usually possible to trace the path of the polypeptide chain and to fit a known amino acid sequence into the map. At this resolution it should be possible to distinguish the density of an alanine side chain from that of a leucine, whereas at 4 A resolution there is little side chain detail. Gross features of functionally important aspects of a structure usually can be deduced at 3 A resolution, including the identification of active-site residues. At 2 A resolution details are sufficiently well resolved in the map to decide between a leucine and an isoleucine side chain, and at 1 A resolution one sees atoms as discrete balls of density. However, the structures of only a few small proteins have been determined to such high resolution. 

Once an electron density map has become available, atoms may be fitted into the map by means of computer graphics to give an initial structural model of the protein. The quality of the electron density map and structural model may be improved through iterative structural refinement but will ultimately be limited by the resolution of the diffraction data. At low resolution, electron density maps have very few detailed features (Fig. 6), and tracing the protein chain can be rather difficult without some knowledge of the protein structure. At better than 3.0 A resolution, amino acid side chains can be recognized with the help of protein sequence information, while at better than 2.5 A resolution solvent molecules can be observed and added to the structural model with some confidence. As the resolution improves to better than 2.0 A resolution, fitting of individual atoms may be possible, and most of the... 

An x-ray analysis will measure the diffraction pattern (positions and intensities) and the phases of the waves that formed each spot in the pattern. These parameters combined result in a three-dimensional image of the electron clouds of the molecule, known as an electron density map. A molecular model of the sequence of amino acids, which must be previously identified, is fitted to the electron density map and a series of refinements are performed. A complication arises if disorder or thermal motion exist in areas of the protein crystal this makes it difficult or impossible to discern the three-dimensional structure (Perczel et al. 2003). 

The degree of accuracy that is attained depends on both the quality of the data and the resolution. At low resolution, 4 to 6 A (0.4 to 0.6 nm), the electron density map reveals little more in most cases than the overall shape of the molecule. At 3.5 A, it is often possible to follow the course of the polypeptide backbone, but there may be ambiguities. At 3.0 A, it is possible in favorable cases to begin to resolve the amino acid side chains and, with some uncertainty, to fit the sequence to the electron density. At 2.5 A, the positions of atoms often can be fitted with accuracy of 0.4 A. To locate atoms to 0.2 A, a resolution of about 1.9 A and very well ordered crystals are necessary. 

Whatever approach is used to deal with the phase problem, the final result will be a pattern of electron density in the unit cell which is then fitted to the amino add sequence of the molecule, which is usually known, to produce a three-dimensional structure. From this structure, a calculated diffraction pattern can be evaluated for comparison with the experimentally observed pattern. A measure of the quality of the determined structure is given by the so-called R factor which is defined by the following equation ... 

Use the known amino-acid sequence to fit the amino-acid side chains to the electron-density map. 

For structures not determined by molecular replacement, the chemical sequence of the protein must be fit into the experimental electron density map (Figure 2.7). This is called model building or chain tracing. As one would expect, the success or failure of chain tracing is dependent upon the quality of the electron density map. Thus, map quality evaluation is very important before one attempts to trace the chain. Good (traceable) electron maps should display most of the following features. 

Since X-rays are scattered by the electrons in a molecule, the outcome of an X-ray crystal structure determination of a protein is a map of electron density in the unit cell, averaged over the > 10 such cells in an individual crystal. The structure arises from a fit of a chemical model to the electron density - the chemical model is determined by the known sequence of the protein (usually) and common bond lengths and bond angles. The goodness of fit of the model to the data is described by an R factor, given by eqn. (5.44), where the structure factors F values) are related to the intensity of the diffraction spot the sum is the sum over all measured spots ... 

A special type of dipole-dipole force arises between molecules that have an H atom bonded to a small, highly electronegative atom with lone electron pairs. The most important atoms that fit this description are N, O, and F. The H—N, H—O, and H—F bonds are very polar, so electron density is withdrawn from H. As a result, the partially positive H of one molecule is attracted to the partially negative lone pair on the N, O, or F of another molecule, and a hydrogen bond (H bond) forms. Thus, the atom sequence that allows an H bond (dotted line) to form is ——A—, where both A and B are N, O, or F. Three examples are... 

After a first complete set of a (hkl) phase angles has been determined with data obtained from the MIR method, or equivalent, an electron density map may then be calculated. If sufficient X-ray diffraction data has been acquired then this map will fit the known primary sequence of the biological macromolecule reasonably well, giving a preliminary model... 

Figure 6.16 Electron Density Map Example of an electron density map generated computationally from electron density data that has been derived by the application of the equations and principles described in the main text from X-ray crystallographic scattering data. The electron density map corresponds with part of the active site of an enzyme LysU (see next Fig. 6.19 Chapters 7 and 8) from the organism Escherichia coli. This electron density map has been "fitted" with the primary sequence polypeptide chain of LysU (colour code - carbon yellow oxygen red nitrogen blue). Once an electron density map has been determined, fitting of the known primary sequence of the biological macromolecule to the electron density map is the final stage that leads to a defined three-dimensional structure (from Onesti et al., 1995, Fig. 9).

Carbonic Anhydrase.—Strandberg and his colleages" have calculated a 2 A resolution electron-density map of human erythrocyte carbonic anhydrase C. A polypeptide chain of 258 amino-acid residues is indicated, and two sequenced fragments have been fitted in positions 1—88 and 224— 258. The structure has a gross shape of 41 x 41 x 47 A and is built essentially of three layers. Seven distorted sections of right-handed a-helix are in the surface layers. In contrast the middle layer is an extensive mainly antiparallel pleated sheet structure with a total twist of 220° and comprising 37% of the total residues. There are aromatic regions between the central sheet and the surface layers. 

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